Numerical Experiments

Abstract

In the previous chapters we have developed and investigated a new concept for the construction of an adaptive FVS where we apply local multiscale techniques to a reference scheme. For scalar conservation laws we have been able to derive an error estimate of the form (5.1). This is based on an a priori error estimate for the discretization error of the reference FVS and the stability of the perturbation error in the sense of (5.3). In [CKMP01] parameter studies have been presented for scalar one-dimensional problems which confirm the analytical results in Chapter 4. In the sequel, we verify that the adaptive concept can also be applied to systems of conservation laws. In particular, we are interested in applications to real-world problems arising from problems in engineering. For this purpose, we present several computations for the two-dimensional Euler equations for a polytropic gas with γ = 1.4, see Example 3. These have been carried out on PC’s with a 600 MHz processor (Pentium III).